Not to be too contrary, but I disagree with this sentiment. First let me say I'm assuming that the OP wants to involve a historical narrative to gain a deeper conceptual understanding of quantum mechanics.

Under that assumption, the interesting thing about QM is that there is very little inherent conceptual justification for the technical descriptions we have of quantum systems other than that 'they work'. Or more precisely, understanding why QM systems are mathematically described in the way they are is still an active area of research.

Therefore, often the closest you can come to a deeper understanding is by tracing how someone stumbled into, or was forced into, using a particular mathematical approach. At least then you are left at the same precipice of knowledge over which experts have been dangling for nearly 100 years now.

I hope that one day we can give deeper explanations for why we have Hilbert spaces and what-not, but until then, learning the history is the closest you can get to understanding why things ended up the way they are on a technical level. And assuming a decent mathematical background, there's no reason you can't also learn the technical detail itself for the first time right along with that historical narrative.